Looped multi-stage thermacoustically driven cryocoolers are considered as promising candidates for applications in liquefaction and recondensation of natural gas. This paper introduces a new configuration capable of cascade power amplification, which could achieves kW-class cooling power and high thermal-to-cold efficiency at natural gas liquefaction temperature. Based on the classic thermoacoustic theory, a three-stage system is numerically investigated. Firstly, the axis distributions of the acoustic power are presented. Then, a comparison is made between this configuration and the previous multiple-coolers configuration The result shows that, this configuration not only has an advantage of structural simplicity and cooling easy-access, but also comparable to the previous configuration in system performance. In addition, emphasis is put on the influence of some key parameters such as area ratio of resonance tube, resonance tube length and heating temperature, which are found to be critical to the engine performance According to the calculation results, a cooling power of 1478 W and a global exergy efficiency of 12.4% is achieved with 923 K heating temperature and 7 MPa pressurized helium gas. This paper provides significant guidance for future experimental work.